fragmented handwritten digit recognition using grading

Fragmented handwritten digit recognition using gradingscheme and fuzzy rules

JYOTISMITA CHAKI1,* and NILANJAN DEY2

1School of Information Technology and Engineering, Vellore Institute of Technology, Vellore, India2Deptartment of Information Technology, Techno India College of Technology, Kolkata, India

e-mail: [email protected]; [email protected]

MS received 20 August 2019; revised 17 May 2020; accepted 5 June 2020

Abstract. The handwritten digit recognition issue turns into one of the well-known issues in machine learning

and computer vision applications. Numerous machine learning methods have been utilized to resolve the

handwritten digit recognition problem. However, sometimes the digit is not completely present in the image due

to issues related to scanning or environmental conditions (light, illumination, dirt, etc.). Although different

efficient methodologies of handwritten digit recognition are proposed, there is not much work done on frag-

mented handwritten digit recognition. The objective of the proposed research work is to handle this circum-

stance to assemble a consistent digit recognition system that can precisely handle three types (English, Bangla,

and Devanagari) of fragmented handwritten digit images. To solve the confusion, a technique is created to

classify handwritten digits based on geometrical functions that are utilized to calculate handwritten digit features

to assess if a digit belongs to a specific class. A grading scheme and a set of specified fuzzy rules determine the

performance of classification. Experiments have been directed on the three familiar datasets, i.e., MNIST

database (English), NumtaDB (Bangla) and Deva numeral database (Devanagari). Since fragmented digit

delivers a lesser amount of information, the work also attempts to create a tentative size threshold above which

outcomes become erratic and whether such thresholds are standardized or vary depending on other factors. Since

the fragmented handwritten digital image does not have a public database, a method is formed to produce

repeatable fragmented handwritten digital images from the entire image. Experimental outcomes validate that

the proposed approach is effective in recognizing fragmented handwritten digits to an acceptable degree of

fragmentation.

Keywords. Fragmented handwritten digit; geometrical functions; fuzzy rules; grading scheme; fragmentation

threshold.

1. Introduction

Handwritten digit recognition is an interesting issue that has

been deeply thought-out for a long time. The motivation

behind why handwritten digit recognition is yet a signifi-

cant area is because of its immense real-world applications

and financial ramifications. The industry requires a decent

recognition rate along with maximum consistency. A

higher recognition rate on handwritten digits rises the

recognition accuracy for digit data, which generally occurs

in numeral strings. When a numeral string is recognized,

the recognition probability of the string is the multiplication

of the recognition probability of every isolated handwritten

digit (presuming that every handwritten digit is appropri-

ately parted from the string by the segmentation procedure).

Moreover, it is impractical to have a handwritten digit

recognition system with 100% recognition exactness.

Hence, the consistency is significantly more vital than the

recognition accuracy in real-life systems.

Although handwritten digit recognition has abundant

applications, the main problem is that their quality turns out

to be degraded because of bad storage conditions and nat-

ural environmental impacts. A damaged handwritten digit

loses its usefulness to deliver recognizing indications since

its shape characteristic may get changed. A classification

system that trusts such features may create unreliable and

unpredictable outcomes. The objective of the proposed

research work is to handle such a state to develop a reliable

handwritten digit recognition system that can precisely

handle three types (English, Bangla, and Devanagari) of

fragmented handwritten digit images. Since fragmented

handwritten digit image also offers less information, the

work will also try to determine a visibility size threshold

beyond which outcomes turn out to be inconsistent and

whether thresholds of this kind are standardized or vary

according to different reasons.*For correspondence

Sådhanå (2020) 45:197 � Indian Academy of Sciences

https://doi.org/10.1007/s12046-020-01410-5Sadhana(0123456789().,-volV)FT3](0123456789().,-volV)

Large numbers of research works are there in the present

literature that utilizes different properties for handwritten

digit recognition. Most of these works though have used

images of the whole digit, an assumption that may not

always be satisfied. Different data modeling methods like

gradient feature [1], triangle feature [2], structural charac-

teristics, modified edge maps, image projections, multi-

zoning, concavities measurement, HoG features [3],

k-means segmentation [4], primitive descriptors [5],

mathematical morphology [6], bat algorithm [7], moment-

based features [8], genetic algorithm [9], mojette transform

[10], stacked generalized auto-encoders [11], etc. are used

by the researchers for the recognition of whole handwritten

digit image. A variety of comparison classifiers and metrics

have been used like support vector machine [1, 12], radial

basis neural network [13], Q-learning deep belief network

[14], spiking neural network [5, 15], AlexNet [16], Goo-

gleNet [17], Multi-Layer Perceptron [18], spiking deep

convolutional neural network [19], convolutional neural

network [20–23], backpropagation neural network [24],

hopfield neural network [25], Naıve Bayes [26], etc.

It is mandatory to mention here that most of the previous

surveys (except [27]) related to the recognition of whole

handwritten digit images and have not come by significant

amount supplementary work which precisely recognizes

fragmented handwritten digit image.

The objective of this study is not only to enhance the

recognition performance but also to ensure maximum

robustness for fragmented handwritten digital recognition

applications. To recognize fragmented handwritten digits, a

geometric function-based grading scheme and the fuzzy

rule-based system is designed. For every fragmented digit,

a separate grade is assigned based on the geometric func-

tion along with the fuzzy rule is proposed according to the

characteristic of the specified digit. Fuzzy Logic is con-

sidered as one of the efficient techniques where smart

behavior is attained through the creation of some parame-

ters’ fuzzy classes. The benefit here is that human under-

standability of the rule and the criteria. Mostly those rules

are specified by a domain specialist and the fuzzy classes.

Many of the previous researchers have used various

machine learning techniques for digit recognition. In

machine learning, a machine is trained to learn a concept by

giving examples, and by developing pattern models to

discriminate between two (or more) classes of objects.

When there is no one specific line discriminating two

classes, or rather, when there is variation between distin-

guishing features of training and testing data (especially in

case of fragmented digit recognition where the training data

consists of the whole image and the testing data is frag-

mented), the fuzzy logic technique is considered more

suitable. Before extracting features from fragmented digits,

some pre-processing steps are proposed to enhance the

recognition rates of the samples. Three familiar datasets,

i.e., MNIST database (English), NumtaDB (Bangla) and

Deva numeral database (Devanagari) are used with the

purpose of validation of the efficacy of the proposed tech-

nique. As there is no public fragmented handwritten digit

database, a procedure is designed to produce the repro-

ducible fragmented handwritten digit images from the

whole one.

The organization of the manuscript is as follows. In

section 2, the proposed method is introduced along with the

block diagram. Experimentations and results are demon-

strated in section 3 and finally, conclusions are given in

section 4.

2. Proposed method

In this paper, a new method is established for the classifi-

cation of fragmented handwritten digit images based on a

grading scheme and fuzzy rules. Figure 1 shows the

flowchart of the proposed method.

Three (English, Bangla, and Devanagari) datasets are

split into testing and training images. As there is no free

dataset for a fragmented handwritten digit image, the

fragmented handwritten digit images are formed from the

whole handwritten digit image. Here the only testing ima-

ges are fragmented. The proposed system is divided into

two stages: pre-processing and classification. Here the

classification accuracy is calculated in two ways:

Figure 1. Flowchart of the proposed method.

197 of 23 Sådhanå (2020) 45:197

considering a grading scheme and grading scheme plus

fuzzy rule-based classification. Before feature extraction,

pre-processing of the handwritten digit images is done to

make it tilt and translation invariant. Then for every frag-

mented testing handwritten digit image, geometrical func-

tions are used to measure characteristics on the handwritten

digits and fuzzy rules are used to determine whether a

fragmented digit belongs to a particular class.

2.1 Creation of fragmented digit image

A new method is established which can be utilized to

generate the reproducible bottom fragmented handwritten

digit image from an entire handwritten digit image inevi-

tably. Specified the image size P� Q. The amount Fð Þ offragmented handwritten digit image that is missing is

dependent on a variable i by the following way:

F ¼ 2

i

� �ð1Þ

Minor fragmented handwritten digits are handled in this

work where a minimum of 70% of the original data is

present; this means that only 30% of the handwritten digit

data is missing. The minor fragmentation can be defined by

using:

i ¼ 20; F ¼ 10%;

i ¼ 18:8; F ¼ 20%;

i ¼ 10; F ¼ 30%

ð2Þ

The scopes for the fragmented handwritten digit image

from the top will be 1 : P½ �; 1 : Q� Q � Fð Þð Þ½ �. The visual

representation of the creation of the fragmented handwrit-

ten digit image is shown in figure 2.

2.2 Pre-processing

Handwritten digit pre-processing may have beneficial

effects on the excellence of feature extraction and the

outcomes of image analysis [28].

The preprocessing task of recognizing handwrit-

ten numbers has been divided into the following steps:

binarization, tilt correction, thinning, and translation cor-

rection. As here the handwritten digit images are frag-

mented, so it is very hard to normalize its orientation and

scaling factor. The raw images have variation in scaling,

orientation, and translation.

2.2 a. BinarizationBinarization is often carried out before the phase of digital

recognition [29]. The input digits should ideally have dual

tones, i.e., white and black (usually 1 and 0). Here 1 rep-

resents foreground (digit) pixels and 0 represents the

background pixels [30].

2.2b. Tilt correctionIrrespective of the size and tilt of a specified digit, a useful

digit recognition system must be able to attain high effi-

ciency. For handwritten digits, tilt, which is characterized

by the slope of the particular writing trend regarding the

vertical line, is one of the main discrepancies in writing

styles. The recognition system must be indifferent to tilt.

The algorithm for tilt correction is described below: The

image is split into three horizontal partitions of the same

height. The centroid of the three partitions is calculated and

linked. The slope of the linking line describes the slope u of

the image. The tilt corrected image is attained by applying

the conversion which is defined by equation (3) to the entire

white pixel coordinate points (x, y) of the original image.

x0 ¼ x� y tan u� dð Þy0 ¼ y

ð3Þ

where x0 and y0 are tilt corrected coordinates and d is the

default tilt.

2.2c ThinningHandwritten digits may have distinct orientations; dig-

its may be curved in shape and may not be parallel to each

other within a page. As a consequence, it is a hard job to

extract and subsequently recognize individual digits in such

papers. Thinning is one of the most important stages in a

single-pixel digit recognition method because of its prop-

erty to hold the original digit shape.

A thinning algorithm is proposed in this manuscript that

can be utilized for thinning handwritten digits. The result-

ing thin digits are the middle lines of the handwritten digits

and therefore this algorithm is invariant to the original

pattern rotations. The thin handwritten digit has a single-

pixel width. The algorithm maintains the topology of the

handwritten digit. This algorithm removes each point on the

outer contour of the handwritten digit to make it single

pixel wide. Three oriented and flipped rules are proposed

which are applied to each pixel of the handwritten digit to

produce the thinned image. The algorithm stops when no

further alterations arise. Figure 3 shows the rules for

thinning.Figure 2. Visual representation of the creation of the fragmented

handwritten digit image.

Sådhanå (2020) 45:197 of 23 197

2.2d Translation correctionAfter the binarization, there would be extra 0’s on all four

sides of an image matrix. The background is contracted

until the handwritten digit image fits perfectly into the

bounding rectangle to stabilize the translation factor. To

achieve this, the standard bilinear transformation is used, by

which, every input bitmap P, of size m� n, is transformed

into a normalized bitmap Q, of size p� q. Both P and Q are

quadrilateral regions.

2.3 Creation of geometrical functions

The proposed geometrical functions are utilized to calculate

the features of the fragmented handwritten digits to decide

whether they belong to a specific class. The functions find

specific geometric attributes such as, in specific direction

openings, closed portion, and lines (vertical, horizontal or

slanted), that distinguish a collection of classes or a certain

class. Most of the functions deliver a way to differentiate

digits that the classification system often confuses. Every

fragmented handwritten digit has some specific geometrical

functions. These functions are designed to recognize

handwritten digits when 30% of the digits are missing from

the bottom.

The depiction is made by subsequent characteristics:

Contour Pixels Detection (CPD): This function

explores in a certain direction to find a digit pixel onto

the contour of the digit (figure 4a). To create this function

first the centroid of the digit is identified. Then, from the

centroid, the contour pixels in 360 directions (anti-

Figure 3. Rules for thinning.

Figure 4. Geometric attributes of digits.

197 of 23 Sådhanå (2020) 45:197

clockwise direction) of the digits are identified at 1�separation.

Top Close Contour (TCC): This function applies CPD

at the centroid of the 3rd row to 10th row of the digit, in

the direction of 0�–360� with separation of 5� and counts

the total number of pixels in the direction of 0�–360�(figure 4b).

Bottom Central Open Contour (BCOC): This function

hunts for openings in 6 direction (250�, 260�, 270�, 280�,290�, 300�) by applying the CPD at the centroid of the 3rd

row to 10th row of the digit and counts the total number of

pixels in above mentioned 6 directions (figure 4c). The

function is applied at the centroid of the first 10 rows of

the handwritten digit, to investigate if the bottom-central

portion of the digit is closed.

Bottom Open Contour (BOC): This function hunts for

openings in direction of 270� by applying the CPD

(figure 4d). The function is applied at the centroid of the

3rd row to the 8th row of the handwritten digit to confirm

if the middle portion of the digit is open.

Bottom-Left Open Contour-1 (BLOC1): This function

applies CPD at the centroid of the 4th row to the18th row

of the digit in the direction of 210�–260� with separation

of 5� to determine whether the bottom-left part of the digit

is open (figure 4e).

Top Open Contour-1 (TOC1): This function applies

CPD at the centroid of the top 10 rows of the digit, in the

direction of 45�–120� with separation of 2� to determine

whether the top part of the digit is open (figure 4f).

Top Open Contour-2 (TOC2): This function applies

CPD at the centroid of the 15th row to the 20th row of the

digit in the direction of 0�–180� with separation of 2� to

determine whether the top part of the bottom portion of the

digit is open (figure 4g).

Top-Right Open Contour (TROC): This function

applies CPD at the centroid of the 3rd row to the10th

row of the digit, in the direction of 0�–45� with separation

of 5� to determine whether the top-right part of the digit is

open (figure 4h).

Bottom-Right Open Contour (BROC): This function

applies CPD at the centroid of the 15th row to the 20th row

of the digit, in the direction of 340�–360� with separation

of 5� to determine whether the bottom-right part of the

digit is open (figure 4i).

Left Open Contour-1 (LOC1): This function applies

CPD at the centroid of the first 10 rows of the digit in the

direction of 110�–260� with separation of 5� to determine

whether the left part of the digit is open (figure 4j).

Left Open Contour-2 (LOC2): This function applies

CPD at the centroid of the 11th row to the 19th row of the

digit, in the direction of 150�–230� with separation of 10�to determine whether the left part of the lower portion of

the digit is open (figure 4k).

Line Detection (LD): The existence of lines in various

parts of the digit image is identified by a line of 8 pixels

height and 1-pixel width that is convolved with the digit

image through in different directions. Horizontal lines are

identified by the following rules: direction 350�–360� and0�–10� is used to detect right horizontal line; direction

170�–180� and 180�–190� is used to detect left horizontal

line. Similarly, vertical lines are identified by the follow-

ing rules: direction 10�–70� is used to detect right slanted

line; direction 80�–90� and 90�–110� is used to detect top

vertical line; direction 195�–245� is used to detect left

slanted line; direction 245�–270� and 270�–280� is used to

detect bottom vertical line (figure 4l). Here 5� separation

is used between angles.

Right-Top-Center Open Contour (RTCOC): This func-

tion applied CPD at the position min xð Þ þ 5 of the 15th to

20th row of the digit in the direction of 70�–120� with

separation of 1� to determine whether the right top center

portion of the digit is open (figure 4m).

Left-Bottom-Center Open Contour (LBCOC): This

function applied CPD at the position max xð Þ � 5 of the

15th to 20th row of the digit in the direction of 220�–270� with separation of 1� to determine whether the

right bottom center portion of the digit is open

(figure 4n).

Figure 5. Pictorial depiction of equation (4).

Figure 6. The process to include a new digit to a pattern set.

Sådhanå (2020) 45:197 of 23 197

Bottom-Left Open Contour-2 (BLOC2): This function

applies CPD at the max xð Þ row of the digit in the direction

of 180�–260� with separation of 2� to determine whether

the bottom-left part from the maximum x-coordinate of the

digit is open (figure 4o).

Right Open Contour (ROC): This function hunts for

openings in direction of 340�–360� and 0�–45� by

applying the CPD (figure 4p). The function is applied at

min xð Þ þ 5 of the 5th row to the 12th row of the

handwritten digit to confirm if the right portion of the

digit is open.

2.4 Classification

The test fragmented digit is classified into two steps: (1)

creation of pattern set and grading the test image and (2)

grading scheme plus fuzzy rules. First to create the pattern

set, the distance between the digit tð Þ of size Q1 � Q2 and a

pattern set Pnð Þ is calculated using equation (4). The pic-

torial depiction of eq. (4) is shown in figure 5.

D Pn; tð Þ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXQ1�1

i¼1

XQ2�1

j¼1

Pn i½ � j½ � � t i½ � j½ �ð Þ2vuut ð4Þ

If the digit image is of the same class as the closest

pattern set and the distance is below the threshold f , thedigit tð Þ is added to that pattern set. Then the digit adjusts

the pattern set using equation (5).

Pk i½ � j½ � ¼ Pk i½ � j½ � � NPat kð Þ þ t i½ � j½ �NPat kð Þ þ 1

ð5Þ

Here NPat kð Þ is the number of digit images that earlier

contributed to the pattern set development. Modification of

the pattern set using training images imposes several

epochs for the training procedure. For each epoch, a random

initial point in the training set is used to avoid dependence

on the outcome cause from the starting point in the training

set. A new pattern set is formed when the distance between

a digit image and its nearest existing pattern set is above a

specified threshold f or when the digit’s class does not

match the nearest pattern set class. By following these steps

twenty-seven pattern sets are formed for nine digits of three

(English, Bangla, and Devanagari) languages. Figure 6

illustrates the procedure of including a new digit to a pattern

set. According to the following example, the new digit

belongs to the pattern set 4.

After creating the pattern set, the Euclidean distance

between the fragmented test digit and the pattern set is

measured and represented with a numeric grade G Dð Þð Þusing a linear function as shown in equation (6).

G Dð Þ ¼ 1� 0:9 D� Dkð Þ=Da ð6ÞA test digit k is categorized in the specific language

(English, Bangla or Devanagari) class with the maximum

grade amongst the pattern sets in the acceptance distance

Dað Þ to digit k.If there is a close distinction in grades between distinct

classes, fuzzy rules are implemented to remove or confirm a

class. The subsequent nine rules for each language i.e.,

(ER0–ER9) for English, (BR0–BR9) for Bangla and (DR0–

DR9) for Devanagari permit to assess whether the digit

belongs to a specific language class (0–9). The inputs of the

rules are geometric attributes calculated from the hand-

written fragmented digits. If the digit is forbidden as a class

member characterized by the rule, the rule delivers a -1

output. Rules provide a value that is positive to categorize

the handwritten digit as a language class member signified

by the rule.

ER0 ¼�1 BCOC[ 0:5

top 3 class of0:9 min vertical line lengthð Þ0:2 �

� �min BCOCð Þ

(

ER1 ¼�1 BCOC[ 0:5

top 3 class of0:9 min horizontal line lengthð Þ0:2 �


(

ER2 ¼�1 LOC1[ 0:3

top 3 class of0:9 max horizontal line lengthð Þ0:2 �

� �min LOC1; LOC2ð Þ

(

ER3 ¼�1 LOC1[ 0:3

top 3 class oftop 2 class of

�1 BOC\0

0:9 min BOCð Þ� �

max horizontal line lengthð Þ0:2 horizontal line length\0:3

8<:

9=; min LOC1; LOC2ð Þ

8><>:

197 of 23 Sådhanå (2020) 45:197

ER4 ¼�1 TOC1[ 0:3

top 2 class of0:9 max horizontal line length þ vertical line lengthð Þ�1 �

� �min TOC1ð Þ

(

ER5 ¼�1 Horizontal line length\0:4

top 3 class of0:9 min vertical line lengthð Þmin vertical line lengthð Þ�1 �

� �max horizontal line lengthð Þ

8<:

ER6 ¼ �1 TROC þ BROCð Þ[ 0:40:9 min TROC þ BROCð Þ

�

ER7 ¼�1 BLOC1[ 0:5

top 4 class of0:9 max horizontal line lengthð Þ�1 horizontal line length\0:6

� �min BLOC1ð Þ

(

ER8 ¼ max TCCþ TOC2gf

ER9 ¼�1 TCC\0:8

top 2 class of0:9 max vertical line lengthð Þ0:2 �

� �max TCCð Þ

(

BR0 ¼�1 BCOC[ 0:5

top 3 class of0:9 max TOC1ð Þ0:2 �


(

BR1 ¼�1 TOC2\0:5

top 4 class of0:9 min BLOC2ð Þ0:2 �

� �max TOC2ð Þ

(

BR2 ¼�1 LOC1[ 0:3

top 3 class of0:9 max horizontal line lengthð Þ0:2 �


(

BR3 ¼�1 RTCOC[ 0:4

top 2 class of0:9 min LBCOCð Þ0:2 �

� �min RTCOCð Þ

(

BR4 ¼ max TCCþ TOC2gf

BR5 ¼�1 BCOC[ 0:3


� TCC[ 0:20:9 min TCCð Þ

� �max TCCð Þ

0:2 TCC\0:7

8<:

9=; min BCOCð Þ

8><>:

BR6 ¼�1 RTCOC[ 0:4

top 2 class of0:9 max LBCOCð Þ0:2 �

� �min RTCOCð Þ

(

BR7 ¼�1 TCC\0:8


� �max TCCð Þ

(

Sådhanå (2020) 45:197 of 23 197

The threshold to develop the pattern set has been adapted

experimentally to a value of 4. Experiments were carried

out utilizing only grades and grade plus fuzzy rules.

The research results are compared with Multilayer Per-

ceptron (MLP) network outcomes as most of the previous

researchers used MLP for the recognition of digit images.

The number of hidden units in the hidden layer network

was changed from 10 to 100� units with a 16:N:10 con-

figuration, where N is the number of hidden units in the

hidden layers. Also, AlexNet, GoogleNet and other rule-

based techniques that are used by the previous researchers

are used to establish the efficiency of the proposed method.

3. Experimentations and results

Experiments were conducted with three different datasets:

70,000 digital English handwritten digit images partitioned

into 10 classes with 7000 images per class obtained from

[31], 20,000 digital Bangla handwritten digit images

BR8 ¼�1 TOC2\0:8

top 2 class of0:9 min TOC1ð Þ0:2 �

� �max TOC2ð Þ

(

BR9 ¼�1 TOC2\0:8


�1 BLOC2\0:80:9 max BLOC2ð Þ

� �min BLOC2ð Þ

0:2 BLOC2[ 0:7

8<:

9=; max TOC2ð Þ

8><>:

DR0 ¼ min BCOCgf

DR1 ¼�1 TCC\0:8


� �max TCCð Þ

(

DR2 ¼�1 LOC1[ 0:3

top 2 class of0:9 min BOCð Þ0:2 �


(

DR3 ¼�1 LOC1[ 0:3

top 3 class of0:9 max LOC1; LOC2ð Þ0:2 �


(

DR4 ¼�1 TOC1[ 0:3

top 2 class of0:9 max BOCð Þ0:2 �


(

DR5 ¼�1 LOC1[ 0:3

top 2 class of0:9 max BOCð Þ0:2 �


(

DR6 ¼ min ROCgf

DR7 ¼�1 TOC1[ 0:3

top 2 class of0:9 min BOCð Þ0:2 �


(

DR8 ¼�1 TOC1[ 0:3

top 3 class of0:9 min TCCð Þ0:2 �

� �max Horizontal Line Lengthð Þ

(

DR9 ¼�1 TCC\0:8

top 2 class of0:9 max LOC2ð Þ0:2 �

� �max TCCð Þ

(

197 of 23 Sådhanå (2020) 45:197

partitioned into 10 classes with 2000 images per class

obtained from [32] and 2880 digital Devanagari handwrit-

ten digit images partitioned into 10 classes with 288 images

per class obtained from [33]. The 64-bit operating system

(Windows 7) with MATLAB software package R2009a and

4 GB RAM was used to test the proposed solution. Of the

collected digit images, 80% were for training purposes and

the remaining 20% images were for testing in terms of their

scaling and orientation variation. Figure 7 shows the Eng-

lish (figure 7a), Bangla (figure 7b) and Devanagari (fig-

ure 7c) digit sample used in the training dataset, with 5

samples per class.

3.1 Creation of fragmented digits

From the testing samples, fragmented (10%, 20% and 30%

digit pixels cropped from the bottom) digit images were

created as designated before. The pictorial representation of

some of the fragmented (30%) test English handwritten

digit images is shown in figure 8. The same technique is

used to create the Bangla and Devanagari fragmented

digits.

3.2 Pre-processing

Before extracting the features from the digit images, the

training and testing images were pre-processed to correct

the degradation of the image. First, the images are bina-

rized. Then the tilt correction, thinning and translation

correction is done as described before. Figure 9 provides an

example of the outcome of the pre-processed module. The

fragmented images are resized to 20 9 28 pixels and the

whole digits are resized to 28 9 28 pixels.

3.3 Modeling the classification scheme

Classification is done in 4 ways to test the efficiency of the

proposed method: (1) Using only grading scheme, (2)

Using fuzzy ? grading scheme when for the recognition of

whole digits (i.e., both training and the testing dataset

contains whole digit image data), (3) Using

fuzzy ? grading scheme when for the recognition of frag-

mented digits (i.e., training and the testing dataset contains

whole and fragmented digit image data respectively) and

(4) Using fuzzy ? grading scheme when for the recogni-

tion of fragmented digits (i.e., both training and the testing

dataset contains fragmented digit image data).

3.3a Classification using only the grading schemeFirst, the classification is performed only considering the

grading scheme. Figure 10 demonstrates the percentage

Figure 7. Training dataset digit sample.

Figure 8. (a) Whole handwritten digit image, (b) 30% frag-

mented digit image.

Figure 9. (a) Binarized image, (b) Tilt corrected, (c) Thinningand (d) Translation corrected.

Sådhanå (2020) 45:197 of 23 197

overall performance classification outcomes acquired by

considering only the grading scheme on the 20% frag-

mented testing digit database for different acceptance dis-

tance [0.0–1.2]. Considering Da ¼ 0:7, the highest outcome

for grading classification achieved which is 80%, 75.8%

and 83.8% for English, Bangla and Devanagari fragmented

testing digit respectively. It can be noted that the case of the

nearest pattern set classification is acquired for case

Da ¼ 0. The classification rate for this case attained is 72%

(English), 68% (Bangla) and 75% (Devanagari).

The confusion matrix for the classification of English,

Bangla, and Devanagari fragmented (20%) digit images

using grading scheme is shown in figures 11a–c,

respectively.

3.3b Classification of whole digits (training and the testingdataset contains whole digit images) using fuzzy ? gradingscheme

After that, the classification outcome is acquired by

considering the grading scheme plus hierarchical fuzzy

rule-based method on English, Bangla and Devanagari

handwritten digits as mentioned when there is no frag-

mentation in both training and testing digits.

The classification procedure of a single English digit

from each class is shown here.

Digit-0:Step 1: The bottom central open contour is applied to each

digit. If the obtained membership value is greater than 0.5,

the digit is forbidden as the class member of digit-0. The

top three classes (maximum grade value) are selected based

on the minimum value of BCOC (figure 12a).

Step 2: Vertical line length is calculated from the three

classes obtained from step 1. The digit having minimum

vertical line length is considered as digit-0 (figure 12b).

Digit-1Step 1: The bottom central open contour is applied to each

digit. If the obtained membership value is greater than 0.5,

Figure 10. Classification of fragmented digits using the grading

scheme.

Figure 11. Confusion matrix representation using the grading

scheme.

197 of 23 Sådhanå (2020) 45:197

the digit is forbidden as the class member of digit-1. The

top three classes (maximum grade value) are selected based

on the minimum value of BCOC (figure 13a).

Step 2: Horizontal line length is calculated from the three


horizontal line length is considered as digit-1 (figure 13b).

Digit-2Step 1: Left open contour-1 is applied to each digit. If the

obtained membership value is greater than 0.3, the digit is

forbidden as the class member of digit-2. The top three

classes (maximum grade value) are selected based on the

minimum value of LOC1 and LOC2 (figure 14a).


classes obtained from step 1. The digit having maximum

horizontal line length is considered as digit-2 (figure 14b).

Digit-3Step 1: Left open contour-1 is applied to each digit. If the


forbidden as the class member of digit-3. The top three


minimum value of LOC1 and LOC2 (figure 15a).

Figure 12. Classification procedure of fragmented Digit-0.




Sådhanå (2020) 45:197 of 23 197


classes obtained from step 1. If the obtained membership

value is less than 0.3, the digit is not considered as the class

member of digit-3. The top two classes are selected based

on the maximum horizontal line length (figure 15b).

Step 3: Bottom open contour is applied to the two classes

obtained from step 2. The digit having minimum BOC is

considered as digit-3 (figure 15c).

Digit-4Step 1: Top open contour-1 is applied to each digit. If the


forbidden as the class member of digit-4. The top two


minimum value of TOC1 (figure 16a).

Step 2: Horizontal and vertical line length is calculated

from the two classes obtained from step 1. The digit having

maximum (Horizontal ? Vertical) line length is considered

as digit-4 (figure 16b).

Digit-5Step 1: Horizontal line length is calculated for each digit.

If the obtained membership value is less than 0.4, the

digit is forbidden as the class member of digit-5. The top

three classes (maximum grade value) are selected based

on the maximum value of horizontal line length

(figure 17a).

Step 2: Vertical line length is calculated from the three



Digit-6Step 1: Top right and bottom right open contour are cal-

culated for each digit. If the obtained membership value is

greater than 0.4, the digit is forbidden as the class member

of digit-6.

Step 2: The digit having the minimum top right and bottom

right open contour (maximum grade value) is considered as

digit-6 (figure 18).

Digit-7Step 1: Bottom left open contour is applied to each digit. If

the obtained membership value is greater than 0.5, the digit

is forbidden as the class member of digit-7. The top four

Figure 16. Classification procedure of fragmented Digit-4. Figure 17. Classification procedure of fragmented Digit-5.



197 of 23 Sådhanå (2020) 45:197


minimum BLOC1 value (figure 19a).

Step 2: Horizontal line length is calculated from the four

classes obtained from step 1. If the obtained membership

value is less than 0.6, the digit is not considered as the class

member of digit-7. The digit having maximum horizontal

line length is considered as digit-7 (figure 19b).

Digit-8Step 1: Top close contour and top open contour-2 are

applied to each digit. The digit having a maximum number

of pixels in (TCC?TOC2) (maximum grade value) is

considered as digit-8 (figure 20).

Digit-9Step 1: The top close contour feature vector is constructed

from each digit. If the obtained membership value is less

than 0.8, the digit is forbidden as the class member of digit-

9. The top two classes (maximum grade value) are selected

based on the maximum TCC value (figure 21a).

Step 2: Vertical line length is calculated from the four

classes obtained from step 1. The digit having maximum


The same procedure is applied for Bangla and Devana-

gari language for the classification of whole digits as

mentioned in section 2.4.

The classification results are listed in table 1. The

recognition rates are 94.8%, 94% and 94.8% for English,

Bangla, and Devanagari digits, respectively. The confusion

matrix for the classification of three types of whole digit

images is shown in figures 22, 23 and 24 respectively.

3.3c Classification of fragmented digits (training and thetesting dataset contains the whole and fragmented imagedata respectively) using fuzzy ? grading scheme

After that, the classification outcome is acquired by

considering the grading scheme plus hierarchical fuzzy

rule-based method on the 20% fragmented testing digit

database for the acceptance distance 0.7.

From each of the entire English handwritten digit test

samples, three types of fragmented images were gener-

ated. The percentages of fragmentation were 30%, 20%,

and 10%. Table 2 shows the overall accuracy of the

three types of fragmented images. The class label out-

puts of fragmented (20%) digit-0 images are shown in

figure 25. This plot contains the membership values of

digit 0, 1 and 7. Class labels 1–100 is for digit-0, class

labels 101–200 is for digit-1, class labels 201–300 is for

digit-7.

The class label outputs of fragmented (20%) digit-1

images are shown in figure 26. This plot contains the

membership values of digit 0, 1 and 7. Class labels 1–100 is

for digit-0, class labels 101–200 is for digit-1, class labels

201–300 is for digit-7.








membership values of digit 2 and 3. Class labels 1–100 is

for digit-2, class labels 101–200 is for digit-3.Figure 20. Classification procedure of fragmented Digit-8.


Table 1. The accuracy percentage of three types of whole digit

images using the grading scheme and fuzzy rules.

Class

Language

English Bangla Devanagari

Digit-0 93 95 97

Digit-1 96 92 96

Digit-2 92 94 92

Digit-3 94 93 94

Digit-4 93 96 95

Digit-5 95 91 93

Digit-6 96 94 92

Digit-7 97 97 95

Digit-8 95 96 97

Digit-9 97 92 97

Sådhanå (2020) 45:197 of 23 197




for digit-1, class labels 101–200 is for digit-4.






Figure 22. Confusion matrix representation for English whole

digit images recognition using the grading scheme plus fuzzy

rules.

Figure 24. Confusion matrix representation for Devanagari

whole digit images recognition using the grading scheme plus

fuzzy rules.

Table 2. The accuracy percentage of the English fragmented

digit images using the grading scheme and fuzzy rules.

Class

Fragmentation

10% 20% 30%

Digit-0 88 82 78

Digit-1 94 90 85

Digit-2 82 79 70

Digit-3 87 84 72

Digit-4 80 78 70

Digit-5 81 80 63

Digit-6 87 84 76

Digit-7 92 90 85

Digit-8 90 89 80

Digit-9 96 94 86

Figure 25. Classification plot of Digit-0.

Figure 23. Confusion matrix representation for Bangla whole

digit images recognition using the grading scheme plus fuzzy

rules.

197 of 23 Sådhanå (2020) 45:197



membership values of digit 4 and 6 as other classes are

forbidden as the class member of digit-6. Class labels

1–100 is for digit-4, class labels 101–200 is for digit-6.



membership values of digit 3, 5, 7 and 9. Class labels 1–100

is for digit-3, class labels 101–200 is for digit-5, class labels

201–300 is for digit-7 and class labels 301–400 is for digit-

9.



membership values of digit 1, 2, 3, 4, 5, 6, 7, 8 and 9. Class

labels 1–100 is for digit-0, class labels 101–200 is for digit-

1, class labels 201–300 is for digit-2, class labels 301–400

is for digit-3, class labels 401–500 is for digit-4, class labels

501–600 is for digit-5, class labels 601–700 is for digit-6,

class labels 701–800 is for digit-7, class labels 801–900 is

for digit-8 and class labels 901–1000 is for digit-9.









Sådhanå (2020) 45:197 of 23 197




for digit-8, class labels 101–200 is for digit-9.

Table 2 shows the correct recognition rates for English

fragmented (30%, 20% and 10%) handwritten digits which

are 76.5%, 85% and 87.7%, respectively.

From table 2, one can recognize that the appropriate

recognition rate is high if the fragmentation percentage is

low. Besides, the classification rate of the fragmented

images of 10% is better than the fragmented images of 20%

and 30%. This may be due to a huge amount of information

present in that specific fragmented part that contributes to

better recognition.

The confusion matrix for the classification of English

fragmented (20%) digit images using this method is shown

in figure 35.

The fuzzy rule-based hierarchical approach is adapted for

the classification of fragmented Bangla and Devanagari

handwritten digits as mentioned in section 2.4. The clas-

sification procedure is similar to the English fragmented

digit classification. Tables 3 and 4 show the correct

recognition rates for 10%, 20%, and 30% fragmented

Bangla and Devanagari digits respectively. The recognition

rates are 88.2%, 82.4% and 76.1% for Bangla and 92%,

89% and 85.5% for Devanagari fragmented digits. The

confusion matrix for the classification of 20% fragmented

Bangla and Devanagari digit images using this method is

shown in Figures 36 and 37 respectively.

3.3d Classification of fragmented digits (both training andthe testing dataset contains fragmented image data) usingfuzzy ? grading scheme

The fuzzy rule-based hierarchical approach is adapted for

the classification of English, Bangla and Devanagari

handwritten digits as mentioned when both training and

testing digits are 20% fragmented which is listed in table 5.

The recognition rates are 90.5%, 88.7% and 90.9% for

English, Bangla, and Devanagari digits respectively. The

confusion matrix for the classification of three types of

fragmented digit images is shown in figures 38, 39 and 40.

From the above experimentation, it is clear that if the

setup is uniform, i.e., both training and testing images are

either whole or fragmented, the efficiency of the proposed

approach is delivering a better recognition rate.


Figure 35. Confusion matrix representation for English frag-

mented (20%) digit images recognition using the grading

scheme plus fuzzy rules.

Table 3. The accuracy percentage of the Bangla fragmented


Class

Fragmentation

10% 20% 30%

Digit-0 90 85 79

Digit-1 85 79 70

Digit-2 88 80 64

Digit-3 88 81 78

Digit-4 90 84 81

Digit-5 86 79 72

Digit-6 87 81 74

Digit-7 95 90 86

Digit-8 89 85 83

Digit-9 84 80 74

Table 4. The accuracy percentage of the Devanagari fragmented


Class

Fragmentation

10% 20% 30%

Digit-0 96 93 90

Digit-1 93 90 86

Digit-2 88 85 82

Digit-3 87 85 80

Digit-4 94 91 88

Digit-5 91 87 84

Digit-6 90 87 82

Digit-7 94 90 87

Digit-8 95 93 90

Digit-9 92 89 86

197 of 23 Sådhanå (2020) 45:197

3.4 Analysis of the proposed method with otherrelated methods mentioned in the literature

The analysis is conducted by considering the whole digit

images in the training and fragmented (20%) digit images

in the testing dataset. The reason behind the consideration

of this type of dataset is: we don’t have any prior

knowledge of the amount of the fragmentation of the test

digit. As the fragmentation percentage is not known to us,

we can’t make the training images fragmented for the

classification of the fragmented test image.

Figure 41 shows the protocol used for the analysis. Here

English (Q), Bangla (Q) and Devanagari (Q) are the frag-

mented query sample taken from English, Bangla and

Devanagari test set, respectively.

Six types of classifiers are used for the analysis purpose

such as Fuzzy system [5], AlexNet [16], GoogleNet [17],

MLP [18], multi column multi scale CNN [34], Multiob-

jective Harmony Search algorithm [35]. After doing the

pre-processing step, the system is first trained by using a

Figure 36. Confusion matrix representation for 20% fragmented

Bangla digit images recognition using the grading scheme plus

fuzzy rules.

Figure 37. Confusion matrix representation for 20% fragmented

Devanagari digit images using the grading scheme plus fuzzy

rules.

Table 5. The accuracy percentage of three types of fragmented


Class

Language

English Bangla Devanagari

Digit-0 87 91 96

Digit-1 92 85 92

Digit-2 88 89 88

Digit-3 89 86 87

Digit-4 85 91 92

Digit-5 89 86 89

Digit-6 91 88 85

Digit-7 94 95 91

Digit-8 93 90 96

Digit-9 97 86 93


mented (20%) digit images.

Sådhanå (2020) 45:197 of 23 197

particular language training digit samples and respective

training module of the abovesaid classifiers. Then the sys-

tem uses the same classifier to classify the same language

fragmented digit.

The efficiency of the MLP model is tested on the English

fragmented testing database. MLP’s highest overall accu-

racy for English fragmented (20%) digits with the network

configuration 16:70:10 are 70%, for the Bangla dataset with

network configuration 16:87:10 is 65% and for Devanagari

dataset, with network configuration 16:67:10 is 79%. Fig-

ure 42 demonstrates the classification of English frag-

mented (20%) digits using MLP.

Figure 43 illustrates the performance of AlexNet [16]

(figure 43a) and GoogleNet [17] (figure 43b) for English

fragmented (20%) digit classification. The overall accuracy

obtained was 77.1% (English), (64%) Bangla, (78%)

Devanagari and 79% (English), 65% (Bangla), 81%

Figure 39. Confusion matrix representation for Bangla frag-

mented (20%) digit images.

Figure 40. Confusion matrix representation for Devanagari

fragmented (20%) digit images.

Figure 41. Protocol used for analysis; (a) Analysis using Englishdataset, (b) Analysis using Bangla dataset, (c) Analysis using

Devanagari dataset.

Figure 42. Classification results of English fragmented (20%)

digits for various number of hidden units.

197 of 23 Sådhanå (2020) 45:197

(Devanagari) using AlexNet and GoogleNet respectively

for 20% fragmented digits.

The reason behind the low percentage of accuracy using

these two methods is probably due to the variation in

training (whole) and testing (fragmented) data because the

significant variation in training and testing data can degrade

the performance of AlexNet and GoogleNet very quickly

and significantly. AlexNet is also often very computation-

ally expensive, because of the large number of parameters

that are normally present in the fully connected layers of

Alexnet. GoogLeNet shows faster speed and smaller model

size compared to AlexNet. GoogLeNet has computational

efficacy, enabling this model to run on devices with limited

computational resources, particularly with low memory.

In [5], researchers have used four primitive descriptions

(closure which is the closed-contour like shape, the smooth

curve which is not closed, protrusion which contains sharp

bending at certain points and straight-line segment) and

rule-based technique to classify whole digits. But this

technique is not appropriate for the fragmented digit

recognition. Table 6 demonstrates the primitive description

obtained by using this method for one English train and test

sample image from each category. For the other two lan-

guages (Bangla and Devanagari) digits, the same procedure

is adopted.

From table 6 it is clear that the primitive features are not

the same (significant variations exist) for the same class

training and fragmented testing images. Also, intraclass

primitive features variations are there which creates diffi-

culty while using these features to train a system. Table 7

shows some of the intraclass primitive features variations

for English sample digits.

Experimentation is conducted using the approach used in

[5] on three (English, Bangla, and Devanagari) frag-

mented testing database to test the efficiency of the method

and the accuracy obtained is 50%, 42%, and 53% respec-

tively for 20% fragmented images. The reason behind the

low recognition rate can be the intraclass feature variation


mented (20%) digit images using (a) AlexNet and (b) GoogleNet.

Table 6. The primitive description obtained for one English

train and test sample image from each class by using the approach

used in [5].

Sådhanå (2020) 45:197 of 23 197

as well as the feature variations of the same class training

and testing dataset.

The proposed method is compared with the methodology

adapted by [34, 35]. In [34] the authors have used multi

column multi scale CNN for the recognition of digits and

obtained good recognition rates for whole digit recognition.

The recognition rate obtained by using the method of [34]

for the English, Bangla and Devanagari fragmented digit is

83.6%, 81.4%, and 75.9% respectively. In [35] authors used

multiobjective Harmony Search algorithm for the recogni-

tion of whole digit images. The recognition rate obtained by

using the method of [35] for the English, Bangla and

Devanagari fragmented digit is 73.3%, 72.8%, and 71.5%

respectively. Figure 44 illustrates the performance of multi-

column multi-scale CNN [34] (figure 44a) and

Table 7. Intraclass primitive features variations for English

digits.


mented (20%) digit images using (a) multi-column multi-scale

CNN and (b) multiobjective Harmony Search algorithm.

Figure 45. Some examples of handwritten digit images that

recognized incorrectly.

197 of 23 Sådhanå (2020) 45:197

multiobjective Harmony Search algorithm [35] (fig-

ure 4(b) for English fragmented digit classification.

The reason behind the low percentage of accuracy using

these two methods [34, 35] is probably due to the variation

in training (whole) and testing (fragmented) data.

The fuzzy rule errors are generated in some cases due

to the lapse of these features. For example, in the case

when the English digit ‘‘3’’ was incorrectly recognized as

English Digit ‘‘5’’, Bangla digit ‘‘1’’ was incorrectly rec-

ognized as Bangla digit ‘‘9’’ etc, the fuzzy rules were not

able to determine clearly. Some examples of handwritten

digit images that recognized incorrectly are shown in

figure 45.

The most common ambiguous pairs are ‘‘5–3’’ and

‘‘4–9’’ for English digits, ‘‘1–9’’ for Bangla digits that have

similar shapes and structures due to the handwriting habits

of individuals. The deteriorated consistency of digital

handwritten digit images such as damaged digits, missing

strokes, noise from assailants and touching strokes. These

cases may be produced by poor handwriting by individuals

or introduced through the scanning procedure, standard-

ization of size, and inappropriate segmentation. With such

unclear and damaged inputs, it is extremely hard for a

computer to produce a correct prediction.

To link the current work with other previous works, it

should be noted that most of the existing methods have

been created for the recognition of the entire digit image. In

[27], the authors have developed the scheme for the clas-

sification of fragmented digit images. Therefore, the

experimentation was carried out utilizing the current

training images and fragmented digit test images to com-

pare the approach of [27] with the proposed approach.

The following performance specifications are calculated:

(1) Correct rate: the ratio of fragmented digits properly

classified, (2) Error rate: the ratio of fragmented digits

incorrectly classified. Table 8 validates the outcomes of the

proposed method compared with the outcomes of

[5, 6, 17, 18, 27] for the recognition of fragmented hand-

written digits. In the proposed approach, a smaller number

of features are used than those of other researches. The

consistency of the result of the proposed method is more

robust than their results for the recognition of fragmented

handwritten digits. The specific geometrical functions and

fuzzy rules for class help in the final classification of the

fragmented handwritten digits. Because the number of final

feature type is small, the rejected rate of this proposed

approach is low.

Fragmented digit (20%) recognition cost is measured by

taking the average time taken to recognize the digit. The

proposed method took 60 min, 20 min, 27 min and to

recognize 14,000 English, 400 Bangla, and 576 Devanagari

fragmented digits respectively.

Table 8. Comparison of Recognition Outcomes.

Approach used Dataset used

Correct rate (%) Error rate (%)

F: 10% F: 20% F: 30% F: 10% F: 20% F: 30%

Dash et al [5] English 54 50 47 46 50 53

Bangla 46 42 39 54 58 61

Devanagari 57 53 49 43 47 51

Krizhevsky et al [16] English 80 77.1 74.3 20 22.9 25.7

Bangla 69 64 62.7 31 36 37.3

Devanagari 82 78 74.1 18 22 25.9

Zhong et al [17] English 85.1 79 75 14.9 21 25

Bangla 71 65 60.4 29 35 39.6

Devanagari 83.7 81 76.1 16.3 19 23.9

Keshta [18] English 78 70 67 22 30 33

Bangla 71 65 60 29 35 40

Devanagari 83 79 72 17 21 28

Ouchtati et al [27] English 61 57 50 39 43 50

Bangla 58 53 49 42 47 51

Devanagari 66 60 56 34 40 44

Sarkhel et al [34] English 85.4 83.6 80.1 14.6 16.4 19.9

Bangla 83.5 81.4 78.5 16.5 18.6 21.5

Devanagari 77.1 75.9 71.6 22.9 24.1 28.4

Gupta et al [35] English 79.5 73.3 69.1 20.5 26.7 30.9

Bangla 75.4 72.8 68.5 24.6 27.2 31.5

Devanagari 78.5 71.5 67.4 21.5 28.5 32.6

Proposed approach English 87.7 85 76.5 12.3 15 23.5

Bangla 88.2 82.4 76.1 11.8 17.6 23.9

Devanagari 92 89 85.5 8 11 14.5

Sådhanå (2020) 45:197 of 23 197

4. Conclusions

A new grading scheme plus a geometric fuzzy model have

been proposed in this paper to address the issue of frag-

mented handwritten digit recognition of three different

languages. This model took the geometrical function as an

automatic extractor of features, enabling the grading

scheme and fuzzy rules to be the predictor of output. The

proposed model’s reliability and efficacy were assessed in

two aspects: accuracy of recognition and overall perfor-

mance of reliability. The MNIST digit dataset (English),

NumtaDB dataset (Bangla) and Deva numeral dataset

(Devanagari) are used to demonstrate the advantage of the

hybrid model is proposed. Compared to other research

works, the proposed approach is producing the best results

for fragmented digit recognition. From the testing out-

comes, it could be confirmed that the recognition result of

10% fragmented digit images is high compared to 20% and

30% category of fragmentations probably due to the more

digit information present in the digit image. Also, it can be

noticed that in this algorithm the main challenging work is

to do the pre-processing of the digit images efficiently. As

the features are based on geometric functions, if the

handwritten digits are not properly pre-processed, the

algorithm can not extract the best geometric features from

the fragmented handwritten digits. Thus, overall recogni-

tion performance can degrade.

Future options for this work may be as follows: (1)

Constructing an effective method that can correctly rec-

ognize fragmented handwritten digital images where only

50% of digital data is viewed; (2) Experiments with other

shape-based techniques; (3) Validation of fragmented digit

images with other classifiers such as Neuro-fuzzy and

Support Vector Machine classifiers and (4) Experimenta-

tion considering fragmentation in eight major directions. To

do this, different geometrical features along with the fuzzy

rules to be developed.

References

[1] Raju G, Moni B S and Nair M S 2014 A novel handwritten

character recognition system using gradient based features

and run length count. Sadhana. 39: 1333–1355[2] Miswan S A, Azmi M S, Arbain N A, Tahir A and Radzid A

R 2018 Rearrangement of coordinate selection for triangle

features improvement in digit recognition. J. Telecommun.Electron. Comput. Eng. (JTEC). 10: 115–119

[3] Nongmeikapam K, Kumar W K, Meetei O N and Tuithung T

2019 Increasing the effectiveness of handwritten Manipuri

Meetei-Mayek character recognition using multiple-HOG-

feature descriptors. Sadhana. 44: 114–118[4] Lee G C, Yeh F H, Chen Y J and Chang T K 2017 Robust

handwriting extraction and lecture video summariza-

tion. Multimed. Tools Appl. 76: 7067–7085

[5] Dash K S, Puhan N B and Panda G 2018 Unconstrained

handwritten digit recognition using perceptual shape prim-

itives. Pattern Anal. Appl. 21: 413–436.[6] Kumar V V, Srikrishna A, Babu B R and Mani M R 2010

Classification and recognition of handwritten digits by using

mathematical morphology. Sadhana. 35: 419–426[7] Boufenar C, Batouche M and Schoenauer M 2018 An

artificial immune system for offline isolated handwritten

arabic character recognition. Evol. Syst. 9: 25–41.[8] Tuba E and Bacanin N 2015 An algorithm for handwritten

digit recognition using projection histograms and SVM

classifier. In 2015 23rd Telecommunications Forum Telfor(TELFOR), pp. 464–467

[9] Das N, Sarkar R, Basu S, Kundu M, Nasipuri M and Basu D

K 2012 A genetic algorithm based region sampling for

selection of local features in handwritten digit recognition

application. Appl. Soft Comput. 12: 1592–1606[10] Singh P K, Das S, Sarkar R, and Nasipuri M 2017

Recognition of handwritten Indic script numerals using

Mojette transform. In: Proceedings of the First InternationalConference on Intelligent Computing and Communication(pp. 459–466)

[11] Sheu J S and Huang Y L 2016 Implementation of an

interactive TV interface via gesture and handwritten numeral

recognition. Multimed. Tools Appl. 75: 9685–9706[12] Mohammadpoor M, Mehdizadeh A and Noghabi H A 2018

A novel method for persian handwritten digit recognition

using support vector machine. Majlesi J. Electr. Eng. 12:63–67

[13] Karayiannis N B and Behnke S 2018 New radial basis neural

networks and their application in a large-scale handwritten

digit recognition problem. In: Recent Advances in ArtificialNeural Networks (pp. 61–116)

[14] Qiao J, Wang G, Li W and Chen M 2018 An adaptive deep

Q-learning strategy for handwritten digit recognition. NeuralNetw. 107: 61–71

[15] Kulkarni S R and Rajendran B 2018 Spiking neural networks

for handwritten digit recognition—supervised learning and

network optimization. Neural Netw. 103: 118–127[16] Krizhevsky A, Sutskever I and Hinton G E 2012 Imagenet

classification with deep convolutional neural networks.

In: Advances in Neural Information Processing Systems(pp. 1097–1105)

[17] Zhong Z, Jin L and Xie Z 2015 High performance offline

handwritten chinese character recognition using googlenet

and directional feature maps. In: 2015 13th InternationalConference on Document Analysis and Recognition (ICDAR)(pp. 846–850)

[18] Keshta I M 2017 Handwritten digit recognition based on

output-independent multi-layer perceptrons. HAND. 8[19] Mozafari M, Ganjtabesh M, Nowzari-Dalini A, Thorpe S J

and Masquelier T 2019 Bio-inspired digit recognition using

reward-modulated spike-timing-dependent plasticity in deep

convolutional networks. Pattern Recognit. 94: 87–95[20] Pratt S, Ochoa A, Yadav M, Sheta A and Eldefrawy M 2019

Handwritten digits recognition using convolution neural

networks. J. Comput. Sci. Coll. 34: 40–46[21] Masood S Z, Shu G, Dehghan A and Ortiz E G 2017 License

plate detection and recognition using deeply learned convo-

lutional neural networks. arXiv preprint arXiv:1703.07330

197 of 23 Sådhanå (2020) 45:197

[22] Zhao H H, and Liu H 2019 Multiple classifiers fusion and

CNN feature extraction for handwritten digits recogni-

tion. Granul. Comput. 1–8[23] Sufian A, Ghosh A, Naskar A and Sultana F 2019 Bdnet:

bengali handwritten numeral digit recognition based on

densely connected convolutional neural networks. arXiv

preprint arXiv:1906.03786

[24] Wang Y, Yao H, Yu W, Wang D, Zhou S and Sun X 2019

Gradual recovery based occluded digit images recogni-

tion. Multimed. Tools Appl. 78: 2571–2586[25] Duan S, Dong Z, Hu X, Wang L, and Li H 2016 Small-world

Hopfield neural networks with weight salience priority and

memristor synapses for digit recognition. Neural Comput.Appl. 27: 837–844

[26] Shamim S M, Miah M B A, Sarker A, Rana M and Al Jobair

A 2018 Handwritten digit recognition using machine learn-

ing algorithms. Glob. J. Comput. Sci. Technol.[27] Ouchtati S, Redjimi M and Bedda M 2015 An offline system

for the recognition of the fragmented handwritten numeric

chains. Int. J. Future Comput. Commun. 4: 33–39[28] Chaki J and Dey N 2018 A Beginner’s Guide to Image

Preprocessing Techniques. CRC Press, Boca Raton

[29] Roy P, Dutta S, Dey N, Dey G, Chakraborty S and Ray R

2014 Adaptive thresholding: a comparative study. In: 2014International Conference on Control, Instrumentation, Com-munication and Computational Technologies (ICCICCT)(pp. 1182–1186)

[30] Satapathy S C, Raja N S M, Rajinikanth V, Ashour A S

and Dey N 2018 Multi-level image thresholding using Otsu

and chaotic bat algorithm. Neural Comput. Appl. 29:

1285–1307

[31] MNIST Dataset (http://yann.lecun.com/exdb/mnist/). Last

access date: 08.03.2019

[32] NumtaDB dataset (https://www.kaggle.com/BengaliAI/

numta)

[33] Deva numeral dataset (https://www.kaggle.com/ashokpant/

devanagari-character-dataset)

[34] Sarkhel R, Das N, Das A, Kundu M and Nasipuri M 2017 A

multi-scale deep quad tree based feature extraction method

for the recognition of isolated handwritten characters of

popular indic scripts. Pattern Recognit. 71: 78–93[35] Gupta A, Sarkhel R, Das N, and Kundu M 2019 Multiob-

jective optimization for recognition of isolated handwritten

Indic scripts. Pattern Recognit. Lett. 128: 318–325

Sådhanå (2020) 45:197 of 23 197

fragmented handwritten digit recognition using grading

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